Question

Find the common difference of an A.P. whose first term is $5$ and the sum of first four terms is half the sum of the next four terms.

Answer 1

Let $d$ is common difference of AP
Now first $4$ terms are $5,5+d,5+2d,5+3d$

and next $4$ terms $5+4d,5+5d,5+6d,5+7d$

Given that, the sum of its first four terms is half the sum of the next four terms.

i.e.,

$5+5+d+5+2d+5+3d=\frac{5+4d+5+5d+5+6d+5+7d}{2}$

$20+6d=\frac{(20+22d)}{2}$
$20+6d=10+11d$
$d=2$

Hence, the common difference of the given A.P. is $2$